C S

T

ANALYSIS OF PERFORMANCE FOR MEMORYLESS PREDISTORTION LINEARIZERS CONSIDERING POWER

AMPLIFIER MEMORY EFFECTS

Hyunchul Ku and J. Stevenson KenneySchool of Electrical and Computer Engineering

Georgia Institute of Technology, Atlanta, GA

IEEE Topical Workshop on PA for Wireless CommunicationsSeptember, 2003San Diego, CA

2

C S

T

Acknowledgements

• This work is supported in part by Danam USA, San Jose, CA.

3

C S

T

Outline

•• IntroductionIntroduction•• New nonlinear PA modelNew nonlinear PA model•• Model verification for real PAModel verification for real PA•• PrePre--D improvement vs. Memory EffectsD improvement vs. Memory Effects•• ConclusionsConclusions

4

C S

T

Memory Effects in PA

• RF frequency response in main signal path • Non-constant impedance in DC bias circuits • Self heating effects at the device level

• Input & Output domain: – Dynamic AM/AM and AM/PM

• Frequency domain:– The asymmetric IMD and spectral regrowth

• Memory Effects: The output depends on the past and current input signal

Reasons

Phenomena

5

C S

T

Memory Effects in Pre-DW

ithou

t Pre

-DW

ith P

re-D

Memoryless PA (Sirenza 0.5W LPA) PA with Memory (Ericsson 45W HPA)

* Result from J. S. Kenney, W. Woo, L. Ding, R. Raich, H. Ku, and G. T. Zhou, “The impact of memory effects on predistortion linearization of RF power amplifiers,” Proc. of the 8th Int. Symp. on Microwave and

Optical Techn., Montreal, Canada, June 19-23 2001, pp. 189–193.

6

C S

T

Research Issues

•• How can we model a PA with memory How can we model a PA with memory effects accurately and efficiently?effects accurately and efficiently?

•• How can we quantify the memory effects How can we quantify the memory effects in PA?in PA?

•• What is the relationship between What is the relationship between degradation of Predegradation of Pre--D and PA memory D and PA memory effects?effects?

7

C S

T

Outline

•• IntroductionIntroduction•• New nonlinear PA modelNew nonlinear PA model•• Model verification for real PAModel verification for real PA•• PrePre--D improvement vs. Memory EffectsD improvement vs. Memory Effects•• ConclusionsConclusions

8

C S

T

PA Behavioral Modelingstart

Model StructureIdentification

Parameter Estimation

Compare model With

Physical system

Success? Final Model

YesNo

Measurement Data

For various signals

DynamicAM/AM, AM/PM /

AsymmetricIMD

AM/AM,AM/PM

AM/AM

PA characterist

ic

Including Long-term

memory effect

Volterra /Wiener

Approach

Systems with memory

Circuit time constant are much smaller than the 1/fm

Complex polynomial or

Quadrature AM/AM model for each I & Q

Quasi-memoryless

system

No phase distortion

Taylor series (real

polynomial)

Memoryless System

CommentModeling Method

PA Model structure depending on

memory effects

9

C S

T

PA with Memory Effects Model I- Volterra Model

∫ ∫ +ττττ−τ−τ−τττ++∫ ∫ τττ−τ−ττ+∫ ττ−τ+=

∞+∞−

∞+∞−

+∞∞−

+∞∞−

+∞∞−

pppp dddtxtxtxhddtxtxhdtxhhty212121

212121211110

)()()(),,,()()(),()()()(

- Volterra Model Drawback

• Complexity: The complexity of the model increases immensely with the length of the system memory and the order of the nonlinearity

• Difficulty in measuring the Volterra kernels: Volterra kernels is not orthogonal, thus each kernels distributions cannot be separated from the total system response

Example: Kernel complexity

10

C S

T

PA with Memory Effects Model IITwo Box Models: One Filter + Memoryless Nonlinear (Wiener Model)

Three Box Models: One Filter + Memoryless Nonlinear + One Filter

• These models have been usually used to capture memory effects in PA modeling (H. B. Poza, A. A. Saleh, T. Vuong, M. S. Muha, and et al.)

• Drawbacks*– These models cannot describe the change of shape in AM/AM and AM/PM

function depending on tone spacing.– These models cannot describe the interaction between the instantaneous

toneC. J. Clark, et al., “Power Amplifier Characterization Using a Two-Tone Measurement Technique,” IEEE

Trans. Microwave Theory Tech., vol. 50, no. 6, pp. 1590-1602, June, 2002

11

C S

T

PA with Memory Effects Model III

∑=

−=n

ii ikxFky

0)]([)(Memory polynomial

Model (MPM)Parallel Wiener model

• These models are simple compared to general Volterra series and complex compared to two or three box model.

• These models compensate the drawbacks for Volterra models and two or three box models

• These models can quantify the memory effects in power amplifier and can apply to linearizer design

12

C S

T

MPM with Sparse Delay Tap (MPMSD)

m n km mk q q q

q ky l a x l d x l d

2( 1)( ) ( )2 1,

0 1

−−−−

−−−−= == == == =

= − ⋅ −= − ⋅ −= − ⋅ −= − ⋅ − ∑∑∑∑∑∑∑∑

• A unit delay tap delay in MPM is replaced with sparse delay taps

• Longer time constant memory effects may be modeled in parallel with short time constant effects using fewer parameters

• MPMSD can improve convergence rate of error compared to MPM

* H. Ku and J. S. Kenney, “Behavioral modeling of power amplifiers considering IMD and spectral regrowth asymmetries,” in IMS 2003, Philadelphia, PA, 2003.

[ ] [ ] [ ]∑ ∑ −⋅−== =

−

−

m

q

n

k

mq

kmqqk dlxdlxaly

0 1

)()1(2)(,12

13

C S

T

Application to PA Modeling

• Easy implementation using linear matrix equation• Adaptive modeling by sliding window• Iterative modeling by adding the branch using output data and error

14

C S

T

Coefficients Extraction for MPMSD

• Coefficients Extraction:

Input complex envelope x Output complex envelope y

- Y: Vector from PA output time data

N: length of sliding window Y

- H(m): A matrix from PA input time data

M+1: The number of branches

[ ]TNlylyly ]1[]1[][ −++=Y( ) ( ) ( ) ( )0

m m m mq m = H H H H

( ) ( )ˆ m m −= ⋅1a H Y

Nx(m+1) matrix Nx1 vector

15

C S

T

Objective: To acquire delay tap set which minimize rms error

where

Delay Tap Extraction for MPMSD

• It is difficult to derive optimal sparse delay taps analytically

• In this case, sequential identification can give simple method to derive delay tap function

( ) { }{ }( )

2( ) ( ) ( ) ( ) ( ) ( )02

| min , m

m m m m m mopt md d= =

dd d E d

{ })()()()()()(2

2

)( ˆRe2ˆˆ mmmmmmm aHYaHHaYYE **** −+=

16

C S

T

•• Memory effect ratio (MER)Memory effect ratio (MER)

– Quantify the magnitude of memory effects– The value is 0 if memoryless case, and increases with

increasing memory effects

•• Memory effect modeling ratio (MEMR) Memory effect modeling ratio (MEMR)

– Quantify the improvement in modeling memory effects in the suggested model.

– This value is 0 when no memory effects are included, and is 1 when all of the memory effects are included.

New Memory Effect Figures of Merit(0) Y 22

E22

YE )0(MER =

22EE )0()(1MEMR m

m −=

17

C S

T

Outline

•• IntroductionIntroduction•• New nonlinear PA modelNew nonlinear PA model•• Model verification for real PAModel verification for real PA•• PrePre--D improvement vs. Memory EffectsD improvement vs. Memory Effects•• ConclusionsConclusions

18

C S

T

Power Amplifier Measurement

• DUT: One LDMOS PA (MRF9180) section of an Danam 880 MHz 50W HPA system

• Test signal: CDMA IS-95B Signal

• Agilent VSA 89410 was used to capture time domain data

• Measured CDMA IS-95B time-domain input and output envelope signals for in-phase and quadrature

19

C S

T

Measurement ResultAM/AM response AM/PM response

Eigh

t-ton

eIS

-95B

20

C S

T

Extracted Parameters & Results

MemorylessMemorylessModelModel

MPMSDMPMSDModelModelWith With

44--additionaladditionalbranchesbranches

21

C S

T

Time Domain Results

RMS Error 0.041 0.016

ML Model MPMSD Model

22

C S

T

Outline

•• IntroductionIntroduction•• New nonlinear PA modelNew nonlinear PA model•• Model verification for real PAModel verification for real PA•• PrePre--D improvement vs. Memory EffectsD improvement vs. Memory Effects•• ConclusionsConclusions

23

C S

T

Pre-D Test Procedure

DesignMemoryless

Pre-D Function

MemorylessPA Model

1. Design memoryless Pre-D based on memoryless model

2. Apply the extracted memoryless Pre-D to PA model with memory

MemorylessPre-D Function

MPMSDPA Model

3. The Performance of Pre-D is analyzed by sweeping MER in the MPMSD model

24

C S

T

Pre-D Design I (p-th order inverse)

23( ) (0.8384 0.1327 ) (0.2007 0.0218 )P x i x i x x= − ⋅ + − ⋅ ⋅

25

4

( ) (0.8384 0.1327 ) (0.2007 0.0218 )

(0.1433 0.0132 )

P x i x i x x

i x x

= − ⋅ + − ⋅ ⋅

+ − ⋅ ⋅

• Using Pre-D based on Polynomial Equation (p-th order inverse)

∑ ⋅==

−−

n

k

kk xxaxf

1

)1(212)(2( 1)

2 11

( )p

kk

kg x b x x−

−=

= ⋅∑1

2( 1) 2( 1)*2 1 2 1 2 1 2 1

1 1 1 1( )

cp p pnl m d

c d l mc d l m

y f z a b b b x x x−

+ − −− − − −

= = = =

= = ⋅ ⋅ ⋅

∑∑ ∑∑

∑ ⋅+=+=∞

+=

−−

1

)1(212

~pk

kk xxaxexyExpected output:

Output:

Compare &Extract coefficients of Pre-D

25

C S

T

Pre-D design II (LUT)

[ ]( ) ( ) exp( ( ( ))LT LT in LT inP x Gain P j Phase P x= ⋅ ⋅

• Using Pre-D based on LUTG

Look Up Table(Gain & Phase)|.|2

Φ PA

• Gain LUT • Phase LUT

26

C S

T

Response for PA with Pre-D

Output without PreD

Output with 3rd order PreD

Output with 5th order PreD

Output with LUT PreD

Linear Response

Output without PreD

Output with 3rd order PreD

Output with 5th order PreD

Output with LUT PreD & Linear Response

• AM/AM Response • AM/PM Response

27

C S

T

ACPR Improvement

• PreD using LUT gives best performance: 20dB improvement in ACPR (IBO=5 dB)

• For p-th order predistorter, the performance increase as order increases. But stability decrease as order increases

PerformanceIncreases

Stability Decreases

28

C S

T

ACPR Improvement Degradation

• By changing MER value (@ 5dB IBO) in model (increasing weighting factor for the additional branches) , compare the ACPR improvements

MER =0%

MER =3%

MER =6%

MER =9%

MER =12%

29

C S

T

Analysis in Frequency Domain

* H. Ku, M. McKinley, and J. S. Kenney, “Quantifying Memory Effects in Power Amplifiers,” IEEE Trans. on Microwave Theory and Tech. vol. 50, no. 12, Dec, 2002.

MER increases

Case 2

Case 1

The range that

memoryless pre-D can improve

Case1

Case2

30

C S

T

Measured

MER vs. Pre-D Improvement

• As MER increases, the improvement decrease : (20dB @ MER= 0%, 14dB@ MER = 9%14dB@ MER = 9%12.5dB @ MER=12%)

: Accurate Prediction for Pre-D improvement

MER=8.89%• Discrepancy between

measured result and simulated result from MPMSD Model=> Because 64% of memory effects are captured in the model (36% are not captured)

4 branch MPMSDModel

By adding more branches

31

C S

T

Conclusions

• Memory polynomial model with sparsely delayed taps (MPMSD) is suggested to model PAs with memory effects such as asymmetric IMD and spectral regrowth: Simple method to implement

• Figure of merits introduced to quantify the amount of memory effects (MER) and quantify the modeling improvement of the suggested model (MEMR).

• Model was extracted for high power LDMOS PA and verified against measurements

• PreD degradation vs. MER is analyzed and simulated